def __init__(self, Nr=0, caller=None):
self.Typ = 'Ellipse'
self.Nr = Nr
# Initialisieren der Werte
# Initialise the values
self.Layer_Nr = 0
self.center = Point(0, 0) # Centre of the geometry
self.vector = Point(1, 0) # Vector A = semi-major axis.
# a = rotation of the ellipse
# http://de.wikipedia.org/wiki/Gro%C3%9Fe_Halbachse
self.ratio = 1 # Verh�ltnis der kleinen zur gro�en Halbachse (b/a)
# Ratio of the minor to major axis (b/a)
# self.AngS = 0 # Startwinkel beim zeichnen eines Ellipsensegments
# Starting angle when drawing an ellipse segment
# self.AngE = radians(360) # Endwinkel (Winkel im DXF als Radians!)
# End angle (angle in radians as DXF!)
# Die folgenden Grundwerte werden sp�ter ein mal berechnet
# The following limits are calculated later
self.length = 0
self.Points = []
self.Points.append(self.center)
# Lesen der Geometrie / Read the geometry
self.Read(caller)
# Zuweisen der Toleranz f�rs Fitting / Assign the tolerance for fitting
tol = g.config.fitting_tolerance
# Errechnen der Ellipse / Calculate the ellipse
self.Ellipse_Grundwerte()
self.Ellipse_2_Arcs(tol)
def arc_arc_intersection(arc1, arc2, refpoint):
# based on
# http://stackoverflow.com/questions/3349125/circle-circle-intersection-points
d = arc1.O.distance(arc2.O)
if d > (arc1.r + arc2.r): # there are no solutions, the circles are separate
return None
elif d + 1e-5 < abs(arc1.r - arc2.r): # there are no solutions because one circle is contained within the other
return None
elif d == 0: # then the circles are coincident and there are an infinite number of solutions
return None
else:
a = (arc1.r**2 - arc2.r**2 + d**2) / (2 * d)
if arc1.r**2 - a**2 < 0:
return None
h = sqrt(arc1.r**2 - a**2)
P2 = arc1.O + a * (arc2.O - arc1.O) / d
p1 = Point(P2.x + h * (arc2.O.y - arc1.O.y) / d,
P2.y - h * (arc2.O.x - arc1.O.x) / d)
p2 = Point(P2.x - h * (arc2.O.y - arc1.O.y) / d,
P2.y + h * (arc2.O.x - arc1.O.x) / d)
intersections = []
if Intersect.point_belongs_to_arc(p1, arc1) and Intersect.point_belongs_to_arc(p1, arc2):
intersections.append(p1)
if Intersect.point_belongs_to_arc(p2, arc1) and Intersect.point_belongs_to_arc(p2, arc2):
intersections.append(p2)
intersections.sort(key=lambda x: (refpoint - x).length_squared())
if len(intersections) > 0:
return intersections[0]
return None
def get_start_end_points(self, start_point, angles=None):
if angles is None:
return self
elif angles:
return self, 0
else:
return self, Point(0, -1) if start_point else Point(0, -1)
def __init__(self, Ps=Point(0, 0), Pe=Point(0, 0), hdl=[]):
"""
Standard method to initialize the class
"""
self.Ps = Ps
self.Pe = Pe
def drawOrientationArrows(self):
rCone = 0.01
rCylinder = 0.004
zTop = 0.05
zMiddle = 0.02
zBottom = -0.03
segments = 20
arrow = GL.glGenLists(1)
GL.glNewList(arrow, GL.GL_COMPILE)
self.drawCone(Point(), rCone, zTop, zMiddle, segments)
self.drawSolidCircle(Point(), rCone, zMiddle, segments)
self.drawCylinder(Point(), rCylinder, zMiddle, zBottom, segments)
self.drawSolidCircle(Point(), rCylinder, zBottom, segments)
GL.glEndList()
self.orientation = GL.glGenLists(1)
GL.glNewList(self.orientation, GL.GL_COMPILE)
self.setColorRGBA(0.0, 0.0, 1.0, 0.5)
GL.glCallList(arrow)
GL.glRotatef(90, 0, 1, 0)
self.setColorRGBA(1.0, 0.0, 0.0, 0.5)
GL.glCallList(arrow)
GL.glRotatef(90, 1, 0, 0)
self.setColorRGBA(0.0, 1.0, 0.0, 0.5)
GL.glCallList(arrow)
GL.glEndList()
def drawWpZero(self):
r = 0.02
segments = 20 # must be a multiple of 4
self.wpZero = GL.glGenLists(1)
GL.glNewList(self.wpZero, GL.GL_COMPILE)
self.setColorRGBA(0.2, 0.2, 0.2, 0.7)
self.drawSphere(r, segments, segments // 4, segments, segments // 4)
GL.glBegin(GL.GL_TRIANGLE_FAN)
GL.glVertex3f(0, 0, 0)
for i in range(segments // 4 + 1):
ang = -i * 2 * pi / segments
xy2 = Point().get_arc_point(ang, r)
# GL.glNormal3f(0, -1, 0)
GL.glVertex3f(xy2.x, 0, xy2.y)
for i in range(segments // 4 + 1):
ang = -i * 2 * pi / segments
xy2 = Point().get_arc_point(ang, r)
# GL.glNormal3f(-1, 0, 0)
GL.glVertex3f(0, -xy2.y, -xy2.x)
for i in range(segments // 4 + 1):
ang = -i * 2 * pi / segments
xy2 = Point().get_arc_point(ang, r)
# GL.glNormal3f(0, 0, 1)
GL.glVertex3f(-xy2.y, xy2.x, 0)
GL.glEnd()
self.setColorRGBA(0.6, 0.6, 0.6, 0.5)
self.drawSphere(r * 1.25, segments, segments, segments, segments)
GL.glEndList()
def bulge2arc(self, Ps, Pe, bulge):
"""
bulge2arc()
"""
c = (1 / bulge - bulge) / 2
# Berechnung des Mittelpunkts (Formel von Mickes!)
# Calculation of the center (Micke's formula)
O = Point((Ps.x + Pe.x - (Pe.y - Ps.y) * c) / 2,
(Ps.y + Pe.y + (Pe.x - Ps.x) * c) / 2)
# Radius = Distance between the centre and Ps
r = O.distance(Ps)
# Kontrolle ob beide gleich sind (passt ...)
# Check if they are equal (fits ...)
# r=O.distance(Pe)
# Unterscheidung f�r den �ffnungswinkel.
# Distinction for the opening angle. ???
if bulge > 0:
return ArcGeo(Ps=Ps, Pe=Pe, O=O, r=r)
else:
arc = ArcGeo(Ps=Pe, Pe=Ps, O=O, r=r)
arc.reverse()
return arc
def drawArrowHead(self, origin, rx, ry, rz, offset):
r = 0.01
segments = 10
zTop = 0 + offset
zBottom = -0.02 + offset
GL.glBegin(GL.GL_TRIANGLE_FAN)
zeroTop = Point3D(0, 0, zTop)
GL.glVertex3f(zeroTop * rx + origin.x, -zeroTop * ry - origin.y,
zeroTop * rz + origin.z)
for i in range(segments + 1):
ang = i * 2 * pi / segments
xy2 = Point().get_arc_point(ang, r).to3D(zBottom)
GL.glVertex3f(xy2 * rx + origin.x, -xy2 * ry - origin.y,
xy2 * rz + origin.z)
GL.glEnd()
GL.glBegin(GL.GL_TRIANGLE_FAN)
zeroBottom = Point3D(0, 0, zBottom)
GL.glVertex3f(zeroBottom * rx + origin.x, -zeroBottom * ry - origin.y,
zeroBottom * rz + origin.z)
for i in range(segments + 1):
ang = -i * 2 * pi / segments
xy2 = Point().get_arc_point(ang, r).to3D(zBottom)
GL.glVertex3f(xy2 * rx + origin.x, -xy2 * ry - origin.y,
xy2 * rz + origin.z)
GL.glEnd()
def calc_bounding_box(self):
"""
Calculated the BoundingBox of the geometry and saves it into self.BB
"""
Ps = Point(x=min(self.Ps.x, self.Pe.x), y=min(self.Ps.y, self.Pe.y))
Pe = Point(x=max(self.Ps.x, self.Pe.x), y=max(self.Ps.y, self.Pe.y))
self.BB = BoundingBox(Ps=Ps, Pe=Pe)
def calc_bounding_box(self, radius=1):
"""
Calculated the BoundingBox of the geometry and saves it into self.BB
@param radius: The Radius of the HoleGeo to be used for BoundingBox
"""
Ps = Point(x=self.Ps.x - radius, y=self.Ps.y - radius)
Pe = Point(x=self.Ps.x + radius, y=self.Ps.y + radius)
self.BB = BoundingBox(Ps=Ps, Pe=Pe)
def Read(self, caller):
"""
Read()
"""
# Assign short name
lp = caller.line_pairs
e = lp.index_code(0, caller.start + 1)
# Assign layer
s = lp.index_code(8, caller.start + 1)
self.Layer_Nr = caller.Get_Layer_Nr(lp.line_pair[s].value)
# X Value
s = lp.index_code(10, s + 1)
x0 = float(lp.line_pair[s].value)
# Y Value
s = lp.index_code(20, s + 1)
y0 = float(lp.line_pair[s].value)
# Radius
s = lp.index_code(40, s + 1)
r = float(lp.line_pair[s].value)
# Searching for an extrusion direction
s_nxt_xt = lp.index_code(230, s + 1, e)
# If there is a extrusion direction given flip around x-Axis
if s_nxt_xt is not None:
extrusion_dir = float(lp.line_pair[s_nxt_xt].value)
logger.debug(self.tr('Found extrusion direction: %s') % extrusion_dir)
if extrusion_dir == -1:
x0 = -x0
O = Point(x0, y0)
# Calculate the start and end values of the circle without clipping
s_ang = -3 * pi / 4
m_ang = s_ang - pi
e_ang = -3 * pi / 4
# Calculate the start and end values of the arcs
Ps = Point(cos(s_ang) * r, sin(s_ang) * r) + O
Pm = Point(cos(m_ang) * r, sin(m_ang) * r) + O
Pe = Point(cos(e_ang) * r, sin(e_ang) * r) + O
# Annexes to ArcGeo class for geometry
self.geo.append(ArcGeo(Ps=Ps, Pe=Pm, O=O, r=r, s_ang=s_ang, e_ang=m_ang, direction=-1))
self.geo.append(ArcGeo(Ps=Pm, Pe=Pe, O=O, r=r, s_ang=m_ang, e_ang=e_ang, direction=-1))
# Length corresponds to the length (circumference?) of the circle
self.length = self.geo[-1].length+self.geo[-2].length
# New starting value for the next geometry
caller.start = s
def Read(self, caller):
"""
This function does read the geometry.
@param caller: The instance which is calling the function
"""
# Assign short name
lp = caller.line_pairs
e = lp.index_code(0, caller.start + 1)
# Assign layer
s = lp.index_code(8, caller.start + 1)
self.Layer_Nr = caller.Get_Layer_Nr(lp.line_pair[s].value)
# X Value
sl = lp.index_code(10, s + 1)
x0 = float(lp.line_pair[sl].value)
# Y Value
s = lp.index_code(20, sl + 1)
y0 = float(lp.line_pair[s].value)
# X Value 2
s = lp.index_code(11, sl + 1)
x1 = float(lp.line_pair[s].value)
# Y Value 2
s = lp.index_code(21, s + 1)
y1 = float(lp.line_pair[s].value)
# Searching for an extrusion direction
s_nxt_xt = lp.index_code(230, s + 1, e)
# If there is a extrusion direction given flip around x-Axis
if s_nxt_xt is not None:
extrusion_dir = float(lp.line_pair[s_nxt_xt].value)
logger.debug(
self.tr('Found extrusion direction: %s') % extrusion_dir)
if extrusion_dir == -1:
x0 = -x0
x1 = -x1
Ps = Point(x0, y0)
Pe = Point(x1, y1)
# Anhängen der LineGeo Klasse für die Geometrie
# Annexes to LineGeo class for geometry ???
self.geo.append(LineGeo(Ps=Ps, Pe=Pe))
# Länge entspricht der Länge des Kreises
# Length corresponding to the length (circumference?) of the circle
self.length = self.geo[-1].length
# Neuen Startwert für die nächste Geometrie zurückgeben
# New starting value for the next geometry
caller.start = s
def calc_O1_O2_k(self, r1, r2, tan_a, theta):
"""
calc_O1_O2_k()
"""
# print("r1: %0.3f, r2: %0.3f, tan_a: %0.3f, theta: %0.3f" %(r1,r2,tan_a,theta))
# print("N1: x: %0.3f, y: %0.3f" %(-sin(tan_a), cos(tan_a)))
# print("V: x: %0.3f, y: %0.3f" %(-sin(theta+tan_a),cos(theta+tan_a)))
O1 = Point(self.Ps.x - r1 * sin(tan_a), self.Ps.y + r1 * cos(tan_a))
k = Point(self.Ps.x + r1 * (-sin(tan_a) + sin(theta + tan_a)),
self.Ps.y + r1 * (cos(tan_a) - cos(tan_a + theta)))
O2 = Point(k.x + r2 * (-sin(theta + tan_a)),
k.y + r2 * (cos(theta + tan_a)))
return O1, O2, k
def calc_bounding_box(self):
"""
Calculated the BoundingBox of the geometry and saves it into self.BB
"""
Ps = Point(x=self.O.x - self.r, y=self.O.y - self.r)
Pe = Point(x=self.O.x + self.r, y=self.O.y + self.r)
# Do the calculation only for arcs have positiv extend => switch angles
if self.ext >= 0:
s_ang = self.s_ang
e_ang = self.e_ang
elif self.ext < 0:
s_ang = self.e_ang
e_ang = self.s_ang
# If the positive X Axis is crossed
if not (self.wrap(s_ang, 0) >= self.wrap(e_ang, 1)):
Pe.x = max(self.Ps.x, self.Pe.x)
# If the positive Y Axis is crossed
if not (self.wrap(s_ang - pi / 2, 0) >= self.wrap(e_ang - pi / 2, 1)):
Pe.y = max(self.Ps.y, self.Pe.y)
# If the negative X Axis is crossed
if not (self.wrap(s_ang - pi, 0) >= self.wrap(e_ang - pi, 1)):
Ps.x = min(self.Ps.x, self.Pe.x)
# If the negative Y is crossed
if not (self.wrap(s_ang - 1.5 * pi, 0) >= self.wrap(
e_ang - 1.5 * pi, 1)):
Ps.y = min(self.Ps.y, self.Pe.y)
self.BB = BoundingBox(Ps=Ps, Pe=Pe)
def Read(self, caller):
"""
Read()
"""
# Assign short name
lp = caller.line_pairs
e = lp.index_code(0, caller.start + 1)
# Assign layer
s = lp.index_code(8, caller.start + 1)
self.Layer_Nr = caller.Get_Layer_Nr(lp.line_pair[s].value)
# X Value
s = lp.index_code(10, s + 1)
x0 = float(lp.line_pair[s].value)
# Y Value
s = lp.index_code(20, s + 1)
y0 = float(lp.line_pair[s].value)
Ps = Point(x0, y0)
self.geo.append(HoleGeo(Ps))
# self.geo.append(LineGeo(Ps=Point(0,0), Pe=P))
# Neuen Startwert für die nächste Geometrie zurückgeben
# New starting value for the next geometry
caller.start = s
def mouseMoveEvent(self, event):
"""
MouseMoveEvent of the Graphiscview. May also be used for the Statusbar.
@purpose: Get the MouseMoveEvent and use it for the Rubberband Selection
@param event: Event Parameters passed to function
"""
if self.mppos is not None:
Point = event.pos() - self.mppos
if Point.manhattanLength() > 3:
# print 'the mouse has moved more than 3 pixels since the oldPosition'
# print "Mouse Pointer is currently hovering at: ", event.pos()
rect = QtCore.QRect(self.mppos, event.pos())
'''
The following is needed because of PyQt5 doesn't like to switch from sign
it will keep displaying last rectangle, i.e. you can end up will multiple rectangles
'''
if self.prvRectRubberBand.width() > 0 and not rect.width() > 0 or rect.width() == 0 or\
self.prvRectRubberBand.height() > 0 and not rect.height() > 0 or rect.height() == 0:
self.rubberBand.hide()
self.rubberBand.setGeometry(rect.normalized())
self.rubberBand.show()
self.prvRectRubberBand = rect
scpoint = self.mapToScene(event.pos())
# self.setStatusTip('X: %3.1f; Y: %3.1f' % (scpoint.x(), -scpoint.y()))
# works not as supposed to
self.setToolTip('X: %3.1f; Y: %3.1f' % (scpoint.x(), -scpoint.y()))
super(MyGraphicsView, self).mouseMoveEvent(event)
def calc_curve(self, n=0, cpts_nr=20):
"""
Berechnen von eine Anzahl gleichm�ssig verteilter Punkte bis zur n-ten Ableitung
"""
# Anfangswerte f�r Step und u
u = 0
step = float(self.Knots[-1]) / (cpts_nr - 1)
Points = []
# Wenn die erste Ableitung oder h�her errechnet wird die ersten
# Ableitung in dem tan als Winkel in rad gespeichert
tang = []
while u <= self.Knots[-1]:
CK = self.bspline_ders_evaluate(n=n, u=u)
# Den Punkt in einem Punkt List abspeichern
Points.append(Point(x=CK[0][0], y=CK[0][1]))
# F�r die erste Ableitung wird den Winkel der tangente errechnet
if n >= 1:
tang.append(atan2(CK[1][1], CK[1][0]))
u += step
return Points, tang
def __init__(self,
startp=Point(),
endp=None,
length=60.0,
angle=50.0,
color=QtCore.Qt.red,
pencolor=QtCore.Qt.green,
startarrow=True):
"""
Initialisation of the class.
"""
self.sc = None
super(Arrow, self).__init__()
self.startp = QtCore.QPointF(startp.x, -startp.y)
self.endp = endp
self.length = length
self.angle = angle
self.startarrow = startarrow
self.allwaysshow = False
self.arrowHead = QPolygonF()
self.setFlag(QGraphicsItem.ItemIsSelectable, False)
self.myColor = color
self.pen = QPen(pencolor, 1, QtCore.Qt.SolidLine)
self.pen.setCosmetic(True)
self.arrowSize = 8.0
def analyse_and_opt(self):
"""
analyse_and_opt()
"""
summe = 0
# Richtung in welcher der Anfang liegen soll (unten links)
# Direction of the top (lower left) ???
Popt = Point(-1e3, -1e6)
# Calculation of the alignment after Gaussian-Elling
# Positive value means CW, negative value indicates CCW
# closed polygon
for Line in self.geo:
summe += Line.Ps.x * Line.Pe.y - Line.Pe.x * Line.Ps.y
if summe > 0.0:
self.reverse()
# Suchen des kleinsten Startpunkts von unten Links X zuerst (Muss neue Schleife sein!)
# Find the smallest starting point from bottom left X (Must be new loop!)
min_distance = self.geo[0].Ps.distance(Popt)
min_geo_nr = 0
for geo_nr in range(1, len(self.geo)):
if self.geo[geo_nr].Ps.distance(Popt) < min_distance:
min_distance = self.geo[geo_nr].Ps.distance(Popt)
min_geo_nr = geo_nr
# Kontur so anordnen das neuer Startpunkt am Anfang liegt
# Order Contour so the new starting point is at the beginning
self.geo = self.geo[min_geo_nr:len(self.geo)] + self.geo[0:min_geo_nr]
def __init__(
self,
text='S',
startp=Point(x=0.0, y=0.0),
):
"""
Initialisation of the class.
"""
QGraphicsItem.__init__(self)
self.setFlag(QGraphicsItem.ItemIsSelectable, False)
self.text = text
self.sc = 1.0
self.startp = QtCore.QPointF(startp.x, -startp.y)
pencolor = QColor(0, 200, 255)
self.brush = QColor(0, 100, 255)
self.pen = QPen(pencolor, 1, QtCore.Qt.SolidLine)
self.pen.setCosmetic(True)
self.path = QPainterPath()
self.path.addText(QtCore.QPointF(0, 0), QFont("Arial", 10 / self.sc),
self.text)
def joinBB(self, other):
"""
Joins two Bounding Box Classes and returns the new one
@param other: The 2nd Bounding Box
@return: Returns the joined Bounding Box Class
"""
if type(self.Ps) == type(None) or type(self.Pe) == type(None):
return BoundingBox(deepcopy(other.Ps), deepcopy(other.Pe))
xmin = min(self.Ps.x, other.Ps.x)
xmax = max(self.Pe.x, other.Pe.x)
ymin = min(self.Ps.y, other.Ps.y)
ymax = max(self.Pe.y, other.Pe.y)
return BoundingBox(Ps=Point(xmin, ymin), Pe=Point(xmax, ymax))
def contains_point(self, point):
"""
Method to determine the minimal distance from the point to the shape
@param point: a QPointF
@return: minimal distance
"""
min_distance = float(0x7fffffff)
ref_point = Point(point.x(), point.y())
t = 0.0
while t < 1.0:
per_point = self.path.pointAtPercent(t)
spline_point = Point(per_point.x(), per_point.y())
distance = ref_point.distance(spline_point)
if distance < min_distance:
min_distance = distance
t += 0.01
return min_distance
def AnalyseAndOptimize(self):
self.setNearestStPoint(Point())
logger.debug(
self.tr("Analysing the shape for CW direction Nr: %s" % self.nr))
if self.isDirectionOfGeosCCW(self.geos):
self.reverse()
logger.debug(self.tr("Had to reverse the shape to be CW"))
self.cw = True
def determineSelectedPosition(self, clicked, forZ, offset):
angleX = -radians(self.rotX)
angleY = -radians(self.rotY)
zv = forZ - offset.z
clickedZ = ((zv + clicked.x * sin(angleY)) / cos(angleY) -
clicked.y * sin(angleX)) / cos(angleX)
sx, sy, sz = self.deRotate(clicked.x, clicked.y, clickedZ)
return Point(sx + offset.x, -sy - offset.y) #, sz + offset.z
def getClickedDetails(self, event):
min_side = min(self.frameSize().width(), self.frameSize().height())
clicked = Point(
(event.pos().x() - self.frameSize().width() / 2),
(event.pos().y() -
self.frameSize().height() / 2)) / min_side / self.scale
offset = Point3D(-self.posX, -self.posY, -self.posZ) / self.scale
tol = 4 * self.scaleCorr / min_side / self.scale
return clicked, offset, tol
def contextMenuEvent(self, event):
"""
Create the contextmenu.
@purpose: Links the new Class of ContextMenu to Graphicsview.
"""
position = self.mapToGlobal(event.pos())
GVPos = self.mapToScene(event.pos())
real_pos = Point(GVPos.x(), -GVPos.y())
menu = MyDropDownMenu(self.scene(), position, real_pos)
def addexprouteen(self):
st = self.expprv
en = Point(g.config.vars.Plane_Coordinates['axis1_start_end'],
g.config.vars.Plane_Coordinates['axis2_start_end'])
self.expcol = QtCore.Qt.darkRed
self.routearrows.append(
Arrow(startp=en, endp=st, color=self.expcol, pencolor=self.expcol))
self.addItem(self.routearrows[-1])
def get_start_end_points(self, start_point, angles=None):
if start_point:
if angles is None:
return self.Ps
elif angles:
return self.Ps, self.s_ang + pi / 2 * self.ext / abs(self.ext)
else:
direction = (self.O - self.Ps).unit_vector()
direction = -direction if self.ext >= 0 else direction
return self.Ps, Point(-direction.y, direction.x)
else:
if angles is None:
return self.Pe
elif angles:
return self.Pe, self.e_ang - pi / 2 * self.ext / abs(self.ext)
else:
direction = (self.O - self.Pe).unit_vector()
direction = -direction if self.ext >= 0 else direction
return self.Pe, Point(-direction.y, direction.x)
def Ellipse_Point(self, alpha=0): # Point(0,0)
"""
Ellipse_Point()
"""
# gro�e Halbachse, kleine Halbachse, rotation der Ellipse (rad), Winkel des Punkts in der Ellipse (rad)
# Semi-major axis, minor axis, rotation of the ellipse (rad), the point in the ellipse angle (rad) ???
Ex = self.a * cos(alpha) * cos(
self.rotation) - self.b * sin(alpha) * sin(self.rotation)
Ey = self.a * cos(alpha) * sin(
self.rotation) + self.b * sin(alpha) * cos(self.rotation)
return Point(self.center.x + Ex, self.center.y + Ey)
def pointisinBB(self, Point=Point(), tol=eps):
"""
Checks if the Point is within the bounding box
@param Point: The Point which shall be ckecke
@return: Returns true or false
"""
x_inter_pos = (self.Pe.x + tol > Point.x) and \
(self.Ps.x - tol < Point.x)
y_inter_pos = (self.Pe.y + tol > Point.y) and \
(self.Ps.y - tol < Point.y)
return x_inter_pos and y_inter_pos